A311824 Coordination sequence Gal.5.158.5 where Gal.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.

1, 4, 8, 13, 17, 21, 25, 30, 37, 43, 47, 51, 56, 60, 62, 64, 70, 77, 81, 85, 89, 94, 99, 103, 109, 115, 120, 124, 126, 128, 132, 137, 143, 149, 153, 158, 163, 167, 171, 175, 182, 188, 190, 192, 196, 201, 205, 209, 215, 222

Offset

0,2

Comments

Note that there may be other vertices in the Galebach list of u-uniform tilings with u <= 6 that have this same coordination sequence. See the Galebach link for the complete list of A-numbers for all these tilings.

Links

Table of n, a(n) for n=0..49.

Brian Galebach, k-uniform tilings (k <= 6) and their A-numbers

Formula

Conjectures from Chai Wah Wu, Nov 19 2025: (Start)

a(n) = 2*a(n-1) - 3*a(n-2) + 4*a(n-3) - 5*a(n-4) + 6*a(n-5) - 7*a(n-6) + 8*a(n-7) - 8*a(n-8) + 8*a(n-9) - 8*a(n-10) + 8*a(n-11) - 8*a(n-12) + 8*a(n-13) - 7*a(n-14) + 6*a(n-15) - 5*a(n-16) + 4*a(n-17) - 3*a(n-18) + 2*a(n-19) - a(n-20) for n > 20.

G.f.: (x^2 + x + 1)^2*(x^16 + 3*x^13 - 3*x^12 + 5*x^11 - 2*x^10 + 4*x^9 - 2*x^8 + 4*x^7 - 2*x^6 + 5*x^5 - 3*x^4 + 3*x^3 + 1)/((x - 1)^2*(x^2 + 1)*(x^4 + 1)*(x^6 - x^5 + x^4 - x^3 + x^2 - x + 1)*(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)). (End)

Crossrefs

Sequence in context: A311821 A311822 A311823 * A311825 A311826 A311827

Adjacent sequences: A311821 A311822 A311823 * A311825 A311826 A311827

Keyword

nonn

Author

Brian Galebach and N. J. A. Sloane, Jun 18 2018

Status

approved